Faraday's law suggests that the current inducted opposes the changing field. (This is also known as Lenz Law). It acts something like an electromagnetic inertia.

Since the middle loop is moving towards the observer, the loop A feels an increasing current. Loop A will thus compensate with a current that acts to decrease the field-change; this current is counter-clockwise by the right-hand rule.

Since the middle loop is moving away from loop B, loop B will want to increase its magnetic field, and thus its current is in the same direction as the middle loop.

Only choice (C) works.

(One can immediately cancel out all but choices (A) and (B) from just a conceptual understanding of Lenz Law.)

Alternate Solutions

secretempire12012-09-04 11:47:18

The best way to think about this problem is the nature does NOT like a change in flux and will attempt to stop it by whatever means necessary.

By the right hand rule (curl your fingers in the direction of the current, the magnetic field points in the direction of your thumb), you know that the magnetic field from the current loop flows outward towards A, and inward from B.

As the middle loop moves towards A, loop A now sees an excess of incoming flux. And remember, nature does not like changing flux, it will try to maintain what it used to have. So to balance out the new flux, loop A will generate a magnetic field in the opposite direction. By the right hand rule, your thumb is now pointing to the right, and your fingers are curling clockwise, indicating a clockwise current.

At the same time, the middle loop is moving away from loop B. Now loop B is seeing a deficiency of flux. Since nature doesn't like to change, loop B will create a magnetic field in the SAME direction to try to boost the flux back up to what it originally was. By the right hand rule, your thumb is pointing to the left, and your fingers are curling counter clockwise, indicating a counter clockwise current.

The best way to think about this problem is the nature does NOT like a change in flux and will attempt to stop it by whatever means necessary.

By the right hand rule (curl your fingers in the direction of the current, the magnetic field points in the direction of your thumb), you know that the magnetic field from the current loop flows outward towards A, and inward from B.

As the middle loop moves towards A, loop A now sees an excess of incoming flux. And remember, nature does not like changing flux, it will try to maintain what it used to have. So to balance out the new flux, loop A will generate a magnetic field in the opposite direction. By the right hand rule, your thumb is now pointing to the right, and your fingers are curling clockwise, indicating a clockwise current.

At the same time, the middle loop is moving away from loop B. Now loop B is seeing a deficiency of flux. Since nature doesn't like to change, loop B will create a magnetic field in the SAME direction to try to boost the flux back up to what it originally was. By the right hand rule, your thumb is pointing to the left, and your fingers are curling counter clockwise, indicating a counter clockwise current.

If a pole approaches a loop, there will be an induced current in such a way that the same pole points back out. If a pole recedes from a loop, the opposite pole will point back out. Then use the right hand rule (thumb along pole, fingers naturally curl in the direction of the current). This can be a little quicker if you're rusty of Lenz's law.

A very useful thing to know (this was pointed out by a user in a problem on the 96 test) is that wires with current in the same direction attract, and wires with current in the opposite directions repel. So that with Lenz's law makes this problem a snap - the middle loop will induce a repelling current in A, and an attracting one in B, in an effort to restore the original state.